Yet another smoothing question - still too many facets
Here's some further things to try:

Autosmooth checkbox under Object Data (right above vertex groups.) This will make edges Sharp based on the specified angle. It is the same effect as Edgesplit, but doesn't actually split your edges.

Use a small amount of of Decimate set to Collapse to merge together nearby points, and/or Planar to fix overlapping faces.

Convert to mesh so that you can properly mark edges with Crease (to control subsurf) or Sharp (to control edge sharpness.)

Use the Intersect (Boolean) command under the Faces menu in edit mode to resolve intersections. Note that this will create some dirty topology that will need to be cleaned up by hand, or with small amounts of Decimate as mentioned above.